What is the derivative of (2x^2-1/(x^{3-x)}) ?

The derivative of (2x^2-1/(x^{3-x)}) is x^{x-3}(2x^2+2x^2ln(x)-2x+(-x+3)/x-ln(x))

What is the first derivative of (2x^2-1/(x^{3-x)}) ?

The first derivative of (2x^2-1/(x^{3-x)}) is x^{x-3}(2x^2+2x^2ln(x)-2x+(-x+3)/x-ln(x))

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\frac{d}{d x} (\frac{2 x ^{2} - 1}{x ^{3 - x}})

x^{x - 3} (2 x^{2} + 2 x^{2} ln (x) - 2 x + \frac{- x + 3}{x} - ln (x))

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} - 1}{x ^{3 - x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 x ^{2} - 1 ) x ^{3 - x} - \frac{d}{d x} ( x ^{3 - x} ) ( 2 x ^{2} - 1 )}{( x ^{3 - x} ) ^{2}}

\frac{d}{d x} (2 x^{2} - 1) = 4 x

\frac{d}{d x} (x^{3 - x}) = x^{3 - x} (- ln (x) + \frac{3 - x}{x})

= \frac{4 x x ^{3 - x} - x ^{3 - x} ( - ln ( x ) + \frac{3 - x}{x} ) ( 2 x ^{2} - 1 )}{( x ^{3 - x} ) ^{2}}

Simplify

\frac{4 x x ^{3 - x} - x ^{3 - x} ( - ln ( x ) + \frac{3 - x}{x} ) ( 2 x ^{2} - 1 )}{( x ^{3 - x} ) ^{2}} : x^{x - 3} (2 x^{2} + 2 x^{2} ln (x) - 2 x + \frac{- x + 3}{x} - ln (x))

= x^{x - 3} (2 x^{2} + 2 x^{2} ln (x) - 2 x + \frac{- x + 3}{x} - ln (x))

\frac{d}{d x} (- 11 (3)^{x - 4})

\int arctan (9 t) d t

\frac{d y}{d x} + y^{7} x + 6 y = 0

(- 1, 1), (2, - 11)

\frac{d}{d x} (e^{x^{4}} + lo g_{3} (π))

What is the derivative of (2x^2-1/(x^{3-x)}) ?
The derivative of (2x^2-1/(x^{3-x)}) is x^{x-3}(2x^2+2x^2ln(x)-2x+(-x+3)/x-ln(x))
What is the first derivative of (2x^2-1/(x^{3-x)}) ?
The first derivative of (2x^2-1/(x^{3-x)}) is x^{x-3}(2x^2+2x^2ln(x)-2x+(-x+3)/x-ln(x))